A light sterile neutrino could be directly produced at colliders  [1]}, [2]}, [3]}, which will lead to the distinct lepton number violation signature [4]}. Meanwhile, if sterile neutrino \(N\)  is lighter than \(W\)  boson, the decay width of sterile neutrino \(\Gamma _N\)  is suppressed by the three-body phase space. Then \(N\)  becomes long-lived and leads to the displaced vertex signature [5]}, [6]}. This signature is very promising to probe the mixing angle \(\theta \)  between the light and sterile neutrinos at present and future colliders [7]}. Thus we focus on light sterile neutrino above the GeV scale in this paper.
